A351960 - OEIS

%I #7 Feb 27 2022 22:24:35

%S 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,8,8,8,8,8,8,9,7,7,7,7,7,9,6,16,6,6,6,6,

%T 16,6,7,9,11,9,9,9,11,9,7,16,6,16,32,16,16,32,16,6,16,15,11,9,11,17,

%U 11,17,11,9,11,15,32,64,32,16,32,10,10,32,16,32,64,32,65,17,13,17,11,17,13,17,11,17,13,17,65

%N Square array A(n,k) = A156552(A005940(1+n) + A005940(1+k)), read by antidiagonals.

%C The indices run as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc. The array is symmetric.

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e The top left corner of the array:

%e      |n= 0    1    2     3    4     5    6    7    8     9    10    11    12

%e -----+--------------------------------------------------------------------------

%e k= 0 |   1,   2,   3,    4,   5,    8,   9,   6,   7,   16,   15,   32,   65,

%e    1 |   2,   3,   4,    5,   8,    7,  16,   9,   6,   11,   64,   17,   14,

%e    2 |   3,   4,   5,    8,   7,    6,  11,  16,   9,   32,   13,   10,   35,

%e    3 |   4,   5,   8,    7,   6,    9,  32,  11,  16,   17,  128,   15,  512,

%e    4 |   5,   8,   7,    6,   9,   16,  17,  32,  11,   10,   19,   64,   21,

%e    5 |   8,   7,   6,    9,  16,   11,  10,  17,  32,   15,   18,   13, 1024,

%e    6 |   9,  16,  11,   32,  17,   10,  13,  64,  15,  128,   23,   18,  129,

%e    7 |   6,   9,  16,   11,  32,   17,  64,  15,  10,   13,  256,   19,   34,

%e    8 |   7,   6,   9,   16,  11,   32,  15,  10,  17,   64,   33,  128,   31,

%e    9 |  16,  11,  32,   17,  10,   15, 128,  13,  64,   19,   12,   33,   20,

%e   10 |  15,  64,  13,  128,  19,   18,  23, 256,  33,   12,   21,   14,   39,

%e   11 |  32,  17,  10,   15,  64,   13,  18,  19, 128,   33,   14,   23, 2048,

%e   12 |  65,  14,  35,  512,  21, 1024, 129,  34,  31,   20,   39, 2048,   25,

%e   13 | 128,  19,  18,   33, 256,   23,  14,  65,  12,   35,   34,   21, 8192,

%e   14 |  35, 512,  21, 1024,  31,   34,  27,  20, 129, 2048,   37,   66,  131,

%e   15 |  64,  13, 128,   19,  18,   33,  12,  23, 256,   65, 1024,   35, 4096,

%e   16 |  11,  32,  17,   10,  15,   64,  19, 128,  13,   18,   65,  256,   27,

%o (PARI)

%o up_to = 104;

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };

%o A351960sq(n,k) = A156552(A005940(1+n)+A005940(1+k));

%o A351960list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0,oo, for(col=0,a, i++; if(i > #v, return(v)); v[i] = A351960sq(col,(a-(col))))); (v); };

%o v351960 = A351960list(up_to);

%o A351960(n) = v351960[1+n];

%Y Cf. A005940, A156552.

%Y Cf. A005408 (main diagonal), A297163 (row/column 0).

%Y Cf. also A341510, A341520, A351961, A351962.

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Feb 26 2022